On the Selection of Boundary Conditions for Droplet Evaporation and Condensation at high Pressure and Temperature Conditions from interfacial Transport Resistivities

Abstract

Understanding suitable boundary conditions for vapor-liquid interfaces is important for the development of physically realistic simulations of evaporation and condensation processes. This work addresses the question whether the inclusion of interfacial temperature jumps is necessary in the modeling of droplet evaporation or condensation. The analysis is divided into two parts. First, a model for coupled heat and mass transfer resistivities for sharp vapor-liquid interfaces is derived from a diffuse interface model. Local resistivities within the interface of n-alkane/nitrogen mixtures are predicted for diffuse interfaces by means of classical density functional theory (DFT) in combination with the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state. Integration over different domains of the local resistivities yields integral resistivities for sharp, or diffuse, interfaces. This allows computation of temperature jumps projected onto sharp interfaces under non-equilibrium conditions. Using this projection we found that interfacial jumps across the vapor-liquid interface are typically small, even for large temperature differences between droplet and ambient vapor. Second, an evaporation model is considered that includes a diffuse transition layer (Knudsen layer) in the order of a few mean free paths around the droplet, where transport processes are described by kinetic molecular theory. The analysis shows that discontinuities in temperature and chemical potential across the interface are important when heat and mass transfer are dominated by molecular collisions. This may occur not only at low pressures, but also at high pressures and temperatures for conditions sufficiently far from global thermodynamic equilibrium, resulting in large heat and mass fluxes and/or for sufficiently small droplets. On a macroscopic scale, the resulting correction to the boundary conditions for classical diffusion-controlled models may be significant at high evaporation or condensation rates.